An inverse variation includes the points (12, 4) and (3, n) . Find n. Write and solve an inverse variation equation to find the answer. n = _____

Identify general form: Given that there is an inverse variation between two variables. Identify the general form of inverse variation. Inverse variation: y = k / xFind constant of variation: We know the inverse variation includes the points (12, 4). Use the first point to find the constant of variation k. Substitute 12 for x and 4 for y in y = k / x. 4 = k / 12Solve for k: Solve the equation to find the value of k. To isolate k, multiply both sides by 12. 4 × 12 = (k / 12) × 12 48 = kWrite inverse variation equation: We have found k = 48. Write the inverse variation equation with the found value of k. Substitute k = 48 in y = k / x. y = 48 / xFind n: The inverse variation equation is y = 48 / x. Find n when x = 3. Substitute 3 for x in y = 48 / x. n = 48 / 3 n = 16

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An inverse variation includes the points $(12,\,4)$ and $(3,\,n)$ . Find $n$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $n = \,\_\_\_\_\_$

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Algebra 1

Write and solve inverse variation equations

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Q. An inverse variation includes the points

(12,\,4)

and

(3,\,n)

. Find

n

\newline

Write and solve an inverse variation equation to find the answer.

\newline

n = \,\_\_\_\_\_

Identify general form: Given that there is an inverse variation between two variables. $\newline$ Identify the general form of inverse variation. $\newline$ Inverse variation: $y = \frac{k}{x}$
Find constant of variation: We know the inverse variation includes the points $(12, 4)$ . Use the first point to find the constant of variation $k$ . Substitute $12$ for $x$ and $4$ for $y$ in $y = \frac{k}{x}$ . $4 = \frac{k}{12}$ .
Solve for k: Solve the equation to find the value of $k$ . $\newline$ To isolate $k$ , multiply both sides by $12$ . $\newline$ $4 \times 12 = \left(\frac{k}{12}\right) \times 12$ $\newline$ $48 = k$
Write inverse variation equation: We have found $k = 48$ . $\newline$ Write the inverse variation equation with the found value of $k$ . $\newline$ Substitute $k = 48$ in $y = \frac{k}{x}$ . $\newline$ $y = \frac{48}{x}$
Find $n$ : The inverse variation equation is $y = \frac{48}{x}$ . Find $n$ when $x = 3$ . Substitute $3$ for $x$ in $y = \frac{48}{x}$ . $n = \frac{48}{3}$ $n = 16$